It succeeded at getting us into a war, but did not succeed at silencing and neutralising criticism and counter evidence. The equivalent would be if the Apollo program was riven by controversy, doubt and criticism from the start, but nevertheless went ahead and rockets were launched but the fakery was ultimately conclusively exposed in the early 1970s, with all the astronauts coming clean and admitting to it.

There was a considerable body of evidence against the WMD story right from the start. Senior CIA personnel were crying foul at how their intelligence was being manipulated for political ends from an early stage, it's just that evidence wasn't enough to stop the war.

Nothing remotely like that ever happened with the Apollo program. There has never been any substantial evidence or testimony against it from within government or NASA, or as Neil pointed out from any foreign specialists or experts, even the Russians. Conversely the WMD story was being challenged internationally from it's conception, as you pointed out yourself.

In terms of challenges, counter evidence and controversy at the time the two cases could not possibly be more starkly utterly different, and that's why they are useful comparisons because the WMD thing shows clearly how government deceptions actually work out.